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高速铁路通信系统作为现代交通工具中的重要组成部分，其通信质量直接影响旅客的乘车体验和铁路运营效率。高速铁路通信系统中，分布式天线系统（Distributed Antenna Systems，DAS）被广泛使用以减轻频繁的手动切换问题，并改善接收信号的信号噪声比（Signal-to-Noise Ratio，SNR）。本文将深入探讨高速铁路通信系统中的功率分配和访问选择策略，并考虑信道状态和交通密度的因素。在高速铁路通信系统的研究中，提出了下行链路功率分配与天线选择相结合（Power Allocation with Antenna Selection，PAWAS）的优化策略，目的在于提高系统的能量效率。通过同时考虑信道状态和交通密度，可以对系统进行有效的功率分配。在此基础上，本文研究了两种典型的地形，即散射稀疏和散射丰富，并探讨了包括时延敏感、时延不敏感和混合交通在内的三种交通模式。研究表明，在小尺度衰落较为严重的情况下，遍历容量会降低，这一点通过定量分析得到证实，并且指出遍历容量与选定的发射天线数目成正比关系。针对不同的交通模式，提出了不同的功率分配和天线选择策略。对于时延敏感的交通，PAWAS可视为与发射天线选择相关的广义信道反转。而在时延不敏感的交通模式下，当选择多个天线时，功率分配可以看作是信道反转，而选择单一天线时，则为传统的水填充算法。对于混合交通模式，提出了通过分别求解其时延敏感和时延不敏感部分的PAWAS来得到最优解。本文通过理论推导和仿真结果验证了所提策略在任意交通密度和信道状态下的平均传输功率最小化的有效性。文章还提到，高速铁路（High-Speed Railway，HSR）在近几十年经历了爆炸性增长，因此对高速铁路通信系统的研究具有重要的现实意义和应用价值。研究中还运用了排队论对不同交通模式下的通信系统性能进行了分析。研究的目的是为高速铁路通信系统提供一个更为高效、稳定和可靠的通信环境，同时也为未来高速铁路通信系统的设计和优化提供了理论依据和技术参考。通过上述内容，我们可以得知高速铁路通信系统中功率分配和访问选择的研究具有以下几个关键的知识点： 1. 高速铁路通信系统中分布式天线系统的作用和优势。 2. 功率分配与天线选择相结合（PAWAS）策略的提出及其对系统能量效率的提升。 3. 信道状态与交通密度在功率分配优化中的重要性。 4. 时延敏感、时延不敏感和混合交通模式对通信系统性能的影响。 5. 不同交通模式下，功率分配和天线选择的不同策略。 6. 遍历容量与选定发射天线数目的关系。 7. 排队论在通信系统性能分析中的应用。 8. 高速铁路通信系统研究对现实世界高速铁路发展的意义。以上内容总结了高速铁路通信系统中关于交通模式、功率分配和访问选择的深入研究，阐述了优化通信系统性能的理论方法，并对实际高速铁路通信系统的设计和优化具有指导意义。

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IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 67, NO. 12, DECEMBER 2018 12273

Toward Trafﬁc Patterns in High-Speed Railwa y

Communication Systems: Power Allocation

and Access Selection

Jiaxun Lu , Ke Xiong , Member, IEEE, Xuhong Chen, and Pingyi Fan , Senior Member, IEEE

Abstract—In high-speed railway communication systems, the

distributed antenna systems are usually employed to mitigate

frequent handover and enhance the signal-to-noise ratio to re-

ceivers. In this case, jointly optimizing downlink power alloca-

tion with antenna selection (PAWAS) can enhance system energy

efﬁciency, while the channel state and trafﬁc density are taken

into account. Besides, two typical kinds of terrains with sparse and

rich scatterings and three trafﬁc patterns including delay-sensitive,

-insensitive, and hybrid trafﬁcs are investigated in this paper. We

show that severe small-scale fading decreases the ergodic capacity,

which is quantitatively analyzed, and proved to be proportional

to the number of selected transmit antennas. In addition, in case

of delay-sensitive trafﬁc, we show that the PAWAS can be viewed

as generalized channel-inversion associated with transmit antenna

selection. In case of delay-insensitive trafﬁc, we show that when

multiple antennas are selected, the power allocation can be viewed

as channel-inversion, whereas when single antenna is selected, it

is traditional waterﬁlling. In case of hybrid trafﬁc, we prove that

the optimal PAWAS method can be given by separately solving

the PAWAS of its delay-sensitive and -insensitive parts. Simulation

results validate our theoretical results and demonstrate that pro-

posed PAWAS can minimize the average transmit power in cases

of arbitrary trafﬁc density and channel states.

Index Terms—Mobility, energy efﬁciency, queuing theory, trafﬁc

pattern, power allocation, antenna selection.

I. INTRODUCTION

N RECENT decades, high-speed railway (HSR) is experi-

encing explosive growth, where distributed antenna systems

(DASs) are usually utilized to mitigate frequent handover and

improve signal to noise ratio (SNR) to receivers [1]–[3]. In the

Manuscript received November 14, 2017; revised June 19, 2018 and August

25, 2018; accepted October 8, 2018. Date of publication October 12, 2018;

date of current version December 14, 2018. This work was supported in part

by the China Major State Basic Research Development Program (973 Program)

under Grant 2012CB316100(2), and in part by the National Natural Science

Foundation of China under Grant 61771283. The review of this paper was

coordinated by Dr. O. Holland. (Corresponding author: Pingyi Fan.)

J. Lu, X. Chen, and P. Fan are with the Department of Electronic Engi-

neering, Tsinghua University, Beijing 100084, China (e-mail:, lujx14@mails.

tsinghua.edu.cn; chenxh13@mails.tsinghua.edu.cn; fpy@tsinghua.edu.cn).

K. Xiong is with the Department of Electronic Engineering, Tsinghua Uni-

versity, Beijing 100084, China, and also with the School of Computer and

Information Technology, Beijing Jiaotong University, Beijing 100084, China

(e-mail:,kxiong@bjtu.edu.cn).

This paper has supplementary downloadable material available at

http://ieeexplore.ieee.org.

Color versions of one or more of the ﬁgures in this paper are available online

at http://ieeexplore.ieee.org.

Digital Object Identiﬁer 10.1109/TVT.2018.2875817

downlink, due to the high mobility of train and large spacing

between adjacent radio antenna units (RAUs), the large-scale

path fading between transmit and receive pairs can be fast time-

varying and widely ﬂuctuant as train running along the railway,

and hence the system energy efﬁciency may also vary dramat-

ically [4]–[7]. In this case, time-domain dynamic resource al-

location based on channel states, such as power allocation and

antenna selection, can effectively maximize the average energy

efﬁciency. For instance, waterﬁlling can be adopted to achieve

the best energy-efﬁciency in time-varying channels, and adap-

tive antenna selection can be used to ﬁnd the best antennas to

transmit with.

In the literatures, most existing works on dynamic resource

allocation considered the power allocation and antenna selec-

tion separately [5]–[10]. For instance, Dong et al. introduced

time-domain power allocation to HSR system by considering

the fairness of system [5], and Zhang et al. extended it by mini-

mizing the average transmit power in cases of delay constraints

[6]. Besides, the authors in [7] related the optimal transmit rates

of delay-sensitive and -insensitive trafﬁcs to speciﬁc total trans-

mit power. The antenna scheme in these papers is single-input-

single-output (SISO). In addition, [8], [9] and [10] provided the

antenna selection strategies of centralized and distributed large-

scale multiple-input-multiple-output (MIMO) by maximizing

the system energy efﬁciency. The considered scenario in these

papers is static.

This paper considers the optimal joint time-domain power

allocation with antenna selection (PAWAS) in dynamic HSR

cases, which minimizes the average transmit power. We focus

on the downlink scenario, where multiple mobile relays (MRs)

are mounted on the carriages, forming the two-hop architecture

and multiple-input channel [2], [6]. At the transmit side, it is

allowed to adaptively select the transmit RAUs. When single

RAU is selected, it is a single-input-multiple-output (SIMO)

transmission, whereas when multiple RAUs are selected, it is a

multiple-input-multiple-output (MIMO) transmission. Besides,

considering the fact that the transmit power at each RAU is con-

strained by their limited module power [11], this paper considers

the transmit scheme where the selected RAUs transmit signals

independently with equal power. Also, note that the problems

on estimating the channel state information (CSI) and mitigat-

ing the interference caused by Doppler spread in HSR systems

have been effectively addressed in the literature [2], [3], [20],

See http://www.ieee.org/publications

standards/publications/rights/index.html for more information.

12274 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 67, NO. 12, DECEMBER 2018

TABLE I

IST OF IMPORTANT NOTATIONS USED IN THIS PAPER

[33]. Based on these previous works, we assume that CSI can be

perfectly acquired in real-time and the Doppler interference can

be ignored. Then, we focus on the optimal time-domain PAWAS

and discuss it in following three different trafﬁc patterns.

The ﬁrst pattern is delay-sensitive trafﬁc, where the arrived

packets need instant service and the delay limit is small com-

pared with the coherence time of channel. In this case, the

queuing process of packets can be modeled by a general G/G/1

model, and the minimal transmit rate satisfying the delay con-

straint is derived. The corresponding optimal PAWAS is shown

to be the channel-inversion associated with antenna selection.

The second pattern is delay-insensitive trafﬁc, where delay is

not a key issue. For instance, popular contents can be cashed in

the MRs to support passengers to get instant access to massive

contents. In this scenario, the delay requirement of sending con-

tents to MRs can be relatively loose [12]–[14]. Noticing that the

energy efﬁciency may vary with the allocated transmit power

and the speciﬁc selected antenna scheme, the optimal power

allocation and antenna selection schemes are coupled. In this

case, we show that the maximum achievable system energy ef-

ﬁciency can be characterized by the equivalent channel gain,

which is the ﬁrst observation of this paper.

Applying the notion of equivalent channel gain, the opti-

mal PAWAS for delay-insensitive trafﬁc is derived. We show

that when MIMO scheme is selected, the optimal power alloca-

tion can be viewed as channel-inversion, whereas when SIMO

scheme is selected, it is traditional waterﬁlling. The third pattern

is hybrid trafﬁc, which is more practical in real systems. In this

case, we prove that the corresponding optimal PAWAS method

can be given by aggregating the PAWAS methods of its delay-

sensitive and -insensitive parts with a supplementary manner.

Nevertheless, the above results are derived in the sparse scat-

tering terrains, such as viaducts, wide plains, etc. This paper

also considers the rich scattering terrains, such as mountain,

tunnels, urban, etc., where the small-scale propagation channel

can be characterized by Nakagami-m channel [15], [16]. The

ergodic capacity loss caused by small-scale fading is quantively

analyzed and shown to be proportional to the number of selected

RAUs. By f ew amendments, previous results in sparse scattering

terrains can be easily extended to rich scattering terrains. Sim-

ulation results show that proposed PAWAS method can always

minimize average transmit power in case of arbitrary trafﬁc

densities and channel states.

The rest of this paper is organized as follows. I n Section II,

the system model is introduced, and the optimal PAWAS method

is mathematically formulated. In Section III, PAWAS strategies

for delay-sensitive, -insensitive and hybrid trafﬁcs in sparse scat-

tering terrains are proposed, respectively. Section I V considers

rich scattering terrains and the corresponding optimal PAWAS

method is proposed. Section V discusses the case where RAUs

are equipped with massive antennas. In Section VI, the validity

of previous theoretical results and the effectiveness of derived

PAWAS are veriﬁed by numerical results. Finally, conclusions

are given in Section VII. Besides, to make the formulation and

discussion in the sequel more clear, a list of important notations

used in this paper is given in Table I.

Notations: (·)

and (·)

denote the transpose of (·) and

max((·), 0), respectively. The symbol I represents the identity

matrix, and E(·) is the diagonal matrix composed by diago-

nal elements (·). det(·) and E(·) are the determinant and the

expected value of (·), respectively.

II. S

YSTEM MODEL AND PROBLEM FORMULATION

This section ﬁrst illustrates the downlink network model of

the considered HSR communication system, where the dis-

tributed RAUs and two-hop architecture are adopted. Then,

the system capacity and channel models are presented, and the

problem on optimal PAWAS is stressed and mathematically for-

mulated.

A. Network Model

Fig. 1 shows the network model of deployed DAS on HSR

systems. At the downlink, a central unit (CU) connected with the

Internet sends data packets to RAUs by optical ﬁbers, and then

RAUs forward the received packets to receivers with the ﬁrst-in-

ﬁrst-out (FIFO) regime [1]–[3]. At the receive side, the two-hop

architecture is adopted to enhance communication quality [1],

LU et al.: TOWARD TRAFFIC PATTERNS IN HIGH-SPEED RAILWAY COMMUNICATION SYSTEMS 12275

Fig. 1. DAS on HSR systems. RAUs are connected to central unit with optical ﬁbers.

Fig. 2. The positions of each node on a reference coordinate system.

[6]. That is, RAUs ﬁrst transmit signals to the mobile relays

(MRs) mounted on the carriage. Then MRs forward signals to

user equipments inside the train. Considering the large spacing

between adjacent RAUs, at most two of them can be achieved

by MRs [3]. Besides, for practical deployment, two MRs are

equipped on the carriage [17].

Fig. 2 depicts the geometry relations of RAUs and MRs on

a reference coordinate system. The dashed-line located at the

middle of two RAUs is denoted as the baseline, and the cross

point of baseline and railway is denoted as the origin. Then,

the distance between the middle of two MRs and origin can

be given by x = vt, where v is the moving velocity of train

and t is the time. The spacing between adjacent RAUs and

MRs are d

and d

, respectively. The vertical distance from

RAUs to the railway is d

. d

i,j

(i, j = 1, 2) denotes the distance

between RAU

and MR

. Because of the regular deployment of

RAUs, the relative positions between MRs and selected RAUs

varies periodically. Hence, this paper considers half duration,

i.e. t ∈ [0,T/2], where T = d

/v.

Note that there exists a dominant strong line-of-sight (LOS)

component in HSR scenarios, which leads to strong channel

correlation between the transmit-to-receive wireless links and

limits the multiplex gain of centralized antenna arrays [18].

This paper mainly considers the case where RAUs are equipped

with single transmit antennas. Then, the case where RAUs are

equipped with massive antenna arrays is discussed in Section V.

It is shown that the corresponding PAWAS method can also be

given by the formulated framework of this paper.

B. Capacity and Channel Models

Recall that due to the large spacing between adjacent RAUs,

at most two of them can be selected to transmit signal to MRs.

Hence, the channel fading matrices corresponding to MIMO

and SIMO schemes can be expressed as

H(t)=



1,1

(t) h

1,2

(t)

2,1

(t) h

2,2

(t)



and H(t)=



1,2

(t)

2,2

(t)



, (1)

respectively. h

i,j

(i, j = 1, 2) is the channel fading coefﬁcient

between RAU

and MR

. Then, the instantaneous system ca-

pacity can be expressed as [19], [20]

C(t)=W log

det



I + E [P (t)/ (N

)] H

(t)H(t)



(2)

where W and P (t) are the available bandwidth and the overall

transmit power of system, respectively. N

is the noise power,

and T

= 1, 2 is the number of selected RAUs. Then, with proper

coding over the random channel states, the achievable ergodic

system capacity can be given by

C(t)=E (C(t)|H(t)) . (3)

In sparse scattering terrains, such as viaduct, ﬂat plain, etc.,

the propagation channel can be considered as an AWGN chan-

nel, and hence the channel fading coefﬁcient h

i,j

(t) can be

characterized by large-scale fading [2]–[7], i.e.

(t)=γ/



(t)



, (4)

where γ is determined by the carrier frequency, antenna heights,

geography, etc. ι ∈ [2, 5] is the path-loss exponent, which is

constant in speciﬁc environment and can be acquired by realistic

measurements [21]. d

i,j

(i, j = 1, 2) follows

i,j

(t)=





− (−1)

i+j

)/2 − (−1)



. (5)

In practice, d

i,j

(t) can be acquired via positioning systems, such

as GPS, Beidou, etc.

However, in rich scattering terrains, the scattering and reﬂec-

tion can not be ignored. In this case, the small-scale fading can

be well modeled with Nakagami-m fading, denoted as n

i,j

(t)

(i, j = 1, 2) [15], [16]. That is, the channel fading coefﬁcient

i,j

(t) can be given by

i,j

(t)=γn

i,j

(t)/



i,j

(t)



. (6)

The power of small-scale fading n

i,j

(t) follows gamma function

Γ(m, Ω). m is the shape factor, and Ω=1 for normalized small-

scale fading.

Also, note that the problems on estimating the channel state

information (CSI) and mitigating the interference caused by

Doppler spread in HSR systems have been effectively addressed

in the literature [2], [3], [20], [33]. Based on these previous

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